Quantitative physical and mathematical methods have been applied to several research problems which potentially are of broad interest to biomedical scientists. These include 1) the use of mathematical and physical techniques to understand the properties and function of biological materials as they relate to cell function, with emphasis on extended polymeric assemblies such as those found on, or near, membrane surfaces or lying between cells; 2) the development of new scattering techniques--using neutrons or light--to examine biological macromolecules when present in concentrated solutions or within highly complexed structures; and 3) the analysis of schemes which utilize light to probe the physiological status of biological tissues. In particular, we have studied various aspects of the rearrangements that take place when clathrin-coated pits, found on the surface of the cells, transform into the coated vesicles which carry accumulated receptor- ligand complexes into a cell during endocytosis. By invoking some basic topological rules, we uncovered stringent constraints which govern the transformations, and thereby were able to infer logical mechanisms for the budding of clathrin-coated vesicles from the cell surface. We also have continued to develop methods to understand how the microstructure of extended polymer networks depends on such factors as polymer concentration and solvent quality, and how the latter might influence how macromolecules migrate through a gel-like substance. In a companion study, mathematical expressions have been derived to explain how data obtained by laser quasielastic light scattering techniques for particles moving through disordered, multiply-scattering immobile matrices depend on the structure of the immobile phase. An equation relating the time dependence of the photon autocorrelation function to the statistical structure of the matrix has been obtained. Finally, recent work on tissue optics has focused on understanding how light passes through tissues of defined thickness, and how the intensity distributions of light discerned in transillumination measurements depended on tissue optical parameters. The derived theory has been applied on an analysis of the resolution limits for optical transillumination of abnormalities which are deeply embedded in tissue.